The purpose of this study is to find out what effects, good and/or bad, intermittent dosing of the drug Selumetinib will have on subjects with uveal melanoma. Selumetinib is a drug that blocks (or turns off) methyl ethyl ketone (MEK), a protein activated in some uveal melanoma cells. Selumetinib is a MEK inhibitor. Blocking MEK may stop the cancer from growing.